Tau-U power analysis

Research question

Q: How strong does a data trend influence the effect-size estimation and power of various tau-u analyzing methods?

Length of A and B phase

Code

design <- design_template(
  n = n_sims,
  start_value = 50,
  s = 10,
  level = 1 * statistic,
  trend = rnorm(n_sims, 0, abs(0.1 / (A_length + B_length))),
  slope = rnorm(n_sims, 0, abs(0.1 / B_length)),
  phase_design = list(A = A_length, B = B_length),
  distribution = "gaussian"
)

iterations <- iterations_template(
  A_length = c(3, 5, 7, 9, 11, 13, 15, 17, 19),
  B_length = c(5, 7, 10, 15, 25, 50),
  statistic = c(0, 1),
  n_sims = 5000
)

out <- create_mc("phaselength.rds", 
                 design, iterations, 
                 force_renew = FALSE)

Example plots

Code

ex_design <- design(
  n = 3,
  start_value = 50,
  s = 10,
  level = 1,
  trend = rnorm(3, 0, abs(0.1 / c(8, 26, 69))),
  slope = rnorm(3, 0, abs(0.1 / c(5, 15, 50))),
  phase_design = list(A = c(3,11,19), B = c(5,15,50)),
  distribution = "gaussian"
)

ex <- random_scdf(ex_design,seed = 124)

ex_fn <- function(x) {
  scplot(x) %>% 
    set_yaxis(limits = c(40,70)) %>%
    add_theme("basic")
}


ex_fn(ex[1])

Code

ex_fn(ex[2])

Code

ex_fn(ex[3])

Power plot

Code

mcplot(out, template = "power")

Code

ggsave(filename = "figure-phaselength.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1)

Power table

Code

mctable(out, wider = "statistic", format = "html", digits = 0)

		statistic 0				statistic 1
A_length	B_length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
3	5	2	1	3	2	51	28	35	51
5	5	3	1	2	3	79	48	48	78
7	5	3	2	3	4	84	55	54	83
9	5	2	2	3	4	85	58	58	84
11	5	3	3	3	4	90	59	58	89
13	5	3	2	2	4	91	56	56	90
15	5	3	2	2	4	93	54	53	92
17	5	3	2	3	4	93	53	53	92
19	5	3	3	3	4	94	51	51	93
3	7	2	1	3	2	60	25	31	60
5	7	3	2	3	3	83	62	53	83
7	7	3	2	3	5	91	75	69	90
9	7	2	2	3	4	93	77	76	91
11	7	3	3	3	5	95	80	77	94
13	7	3	2	2	5	96	80	77	95
15	7	3	3	3	5	97	79	76	96
17	7	3	2	3	5	98	75	76	96
19	7	3	3	3	5	98	76	76	97
3	10	3	0	3	3	72	6	29	72
5	10	3	1	3	3	86	67	57	86
7	10	2	1	3	4	94	83	77	93
9	10	3	2	3	5	96	89	84	94
11	10	3	2	3	5	98	93	89	96
13	10	3	3	4	5	99	93	91	97
15	10	3	2	3	5	99	94	93	98
17	10	3	2	2	5	99	94	92	98
19	10	3	3	3	5	100	94	92	98
3	15	2	0	3	2	76	0	28	76
5	15	3	1	3	3	93	67	55	93
7	15	3	1	3	5	97	89	76	96
9	15	3	1	4	5	99	95	89	97
11	15	3	2	4	5	100	98	94	98
13	15	4	2	4	5	100	99	97	98
15	15	3	2	3	5	100	99	97	98
17	15	3	2	3	5	100	99	98	98
19	15	3	2	3	6	100	100	99	99
3	25	3	0	4	3	83	0	24	83
5	25	3	0	3	4	95	47	47	94
7	25	3	0	4	4	99	88	71	97
9	25	4	1	4	6	100	97	86	97
11	25	3	1	4	5	100	99	94	98
13	25	3	1	4	5	100	100	97	98
15	25	4	2	4	6	100	100	99	98
17	25	4	2	5	6	100	100	99	97
19	25	3	2	4	6	100	100	100	98
3	50	3	0	4	3	86	0	17	86
5	50	3	0	5	4	97	0	34	97
7	50	2	0	4	4	100	66	52	98
9	50	3	0	4	5	100	93	70	98
11	50	3	0	4	5	100	99	83	98
13	50	4	0	5	6	100	100	92	98
15	50	4	1	5	6	100	100	96	98
17	50	4	1	5	6	100	100	98	98
19	50	4	1	5	7	100	100	99	98

Tau plot

Code

mcplot(out,var_y = "es")

Code

ggsave(filename = "figure-phaselength-tau.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1)

Tau table

Code

mctable(out, wider = "statistic", format = "html", var_y = "es")

		statistic 0				statistic 1
A_length	B_length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
3	5	0.00	0.00	0.00	0.00	0.84	0.84	0.45	0.61
5	5	0.00	0.00	0.00	0.00	0.84	0.85	0.47	0.62
7	5	0.00	0.00	0.00	-0.01	0.84	0.85	0.45	0.61
9	5	0.00	0.00	0.00	0.00	0.84	0.84	0.42	0.58
11	5	0.00	0.01	0.00	0.00	0.84	0.84	0.38	0.56
13	5	0.00	0.00	0.00	0.00	0.84	0.84	0.36	0.54
15	5	0.00	0.00	0.00	0.00	0.84	0.84	0.33	0.53
17	5	0.00	0.00	0.00	0.00	0.84	0.84	0.31	0.50
19	5	0.00	0.00	0.00	0.00	0.84	0.84	0.29	0.49
3	7	0.00	0.00	0.00	0.00	0.84	0.84	0.40	0.58
5	7	0.01	0.00	0.01	0.00	0.84	0.84	0.44	0.60
7	7	0.00	0.00	0.00	0.00	0.84	0.84	0.45	0.61
9	7	0.00	0.00	0.00	0.00	0.84	0.85	0.44	0.60
11	7	0.00	0.00	0.00	0.00	0.84	0.84	0.42	0.59
13	7	0.00	-0.01	0.00	0.00	0.84	0.84	0.40	0.58
15	7	0.00	0.00	0.00	0.00	0.84	0.84	0.38	0.56
17	7	0.01	0.00	0.00	0.00	0.84	0.84	0.36	0.55
19	7	0.00	0.00	0.00	0.00	0.84	0.84	0.34	0.54
3	10	0.00	0.00	0.00	0.00	0.84	0.84	0.33	0.52
5	10	0.00	0.00	0.00	0.00	0.84	0.84	0.40	0.57
7	10	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
9	10	0.01	0.01	0.01	0.01	0.84	0.84	0.44	0.59
11	10	0.00	0.00	0.00	0.00	0.84	0.84	0.44	0.60
13	10	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
15	10	0.00	0.01	0.00	0.00	0.84	0.84	0.42	0.59
17	10	0.00	0.00	0.00	0.00	0.84	0.84	0.41	0.58
19	10	0.00	0.00	0.00	0.00	0.84	0.84	0.39	0.57
3	15	0.01	0.01	0.00	0.00	0.84	0.84	0.25	0.46
5	15	0.00	0.00	0.00	0.00	0.84	0.84	0.33	0.52
7	15	0.00	0.00	0.00	0.00	0.84	0.84	0.38	0.56
9	15	0.00	0.00	0.00	0.00	0.84	0.84	0.41	0.57
11	15	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
13	15	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
15	15	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
17	15	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
19	15	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
3	25	0.00	0.00	0.00	0.00	0.84	0.84	0.17	0.37
5	25	0.00	0.00	0.00	0.00	0.84	0.84	0.24	0.44
7	25	0.00	0.00	0.00	0.00	0.84	0.84	0.30	0.49
9	25	0.00	0.00	0.00	0.00	0.84	0.84	0.34	0.52
11	25	0.01	0.01	0.00	0.01	0.84	0.84	0.37	0.54
13	25	-0.01	-0.01	0.00	0.00	0.84	0.84	0.39	0.56
15	25	0.00	0.00	0.00	0.00	0.84	0.84	0.40	0.57
17	25	0.00	0.00	0.00	0.00	0.84	0.84	0.41	0.57
19	25	-0.01	-0.01	0.00	0.00	0.84	0.84	0.42	0.58
3	50	0.00	0.00	0.00	0.00	0.84	0.84	0.09	0.28
5	50	0.00	0.00	0.00	0.00	0.84	0.84	0.14	0.34
7	50	-0.01	-0.01	0.00	0.00	0.84	0.84	0.18	0.38
9	50	0.00	0.00	0.00	0.00	0.84	0.84	0.22	0.41
11	50	0.00	0.00	0.00	0.00	0.84	0.84	0.25	0.45
13	50	0.00	0.00	0.00	0.00	0.84	0.84	0.28	0.47
15	50	0.00	0.00	0.00	0.00	0.84	0.84	0.30	0.49
17	50	0.00	0.00	0.00	0.00	0.84	0.84	0.32	0.51
19	50	0.00	0.00	0.00	0.00	0.84	0.84	0.34	0.52

Intervention strength

Code

design <- design_template(
    n = n_sims,
    start_value = 50,
    s = 10,
    level = level_effect * statistic,
    trend = rnorm(n_sims, 0, 0.1 / length),
    slope = rnorm(n_sims, 0, 0.1 / (length * 2/3)),
    phase_design = list(A = length * 1/3, B = length * 2/3),
    distribution = "gaussian"
)

iterations <- iterations_template(
  level_effect = c(0.25, 0.5, 0.75, 1, 1.25, 1.5),
  length = c(9, 12, 15, 21, 27, 33, 39, 45),
  statistic = c(0,1),
  n_sims = 5000
)

out <- create_mc("interventioneffect-length.rds", 
                 design, iterations,
                 force_renew = FALSE)

Example plots

Code

ex_design <- design(
  n = 3,
  start_value = 50,
  s = 10,
  level = c(0.25, 1, 1.5),
  trend = rnorm(3, 0, abs(0.1 / c(9, 21, 50))),
  slope = rnorm(3, 0, abs(0.1 / c(6, 14, 45))),
  phase_design = list(A = c(3,7,15), B = c(6,14,45)),
  distribution = "gaussian"
)

ex <- random_scdf(ex_design,seed = 124)

ex_fn <- function(x) {
  scplot(x) %>% 
    set_yaxis(limits = c(40,80)) %>%
    add_theme("basic")
}


ex_fn(ex[1])

Code

ex_fn(ex[2])

Code

ex_fn(ex[3])

power plot

Code

mcplot(out, var_x = 2, var_shape = 1, template = "power")

Code

ggsave(filename = "figure-interventioneffect.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1)

power table

Code

mctable(out, wider = "statistic", format = "html", digits = 0)

		statistic 0				statistic 1
level_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
0	9	3	1	2	3	9	3	7	9
0	9	3	1	2	3	21	8	13	21
1	9	3	1	3	3	43	17	22	43
1	9	2	1	2	2	63	26	30	63
1	9	2	1	2	2	81	36	37	81
2	9	2	1	3	2	92	42	40	92
0	12	3	1	3	6	10	3	8	14
0	12	3	1	2	6	31	11	18	33
1	12	3	1	3	6	56	25	31	56
1	12	3	1	3	7	80	44	45	78
1	12	3	1	3	7	93	60	53	89
2	12	3	1	3	7	98	72	58	94
0	15	3	1	3	3	11	6	10	12
0	15	2	1	3	3	34	19	23	34
1	15	2	1	3	3	63	42	40	63
1	15	2	1	3	3	87	68	57	86
1	15	2	1	3	3	97	86	69	96
2	15	3	1	3	3	100	96	75	99
0	21	3	1	3	4	17	9	14	18
0	21	3	1	3	4	50	31	34	50
1	21	3	1	3	4	81	63	57	80
1	21	2	1	3	4	97	89	77	95
1	21	3	1	3	4	100	98	87	98
2	21	3	1	3	4	100	100	92	99
0	27	3	1	3	6	21	10	16	22
0	27	2	1	4	5	60	40	42	60
1	27	3	1	4	5	91	77	71	89
1	27	3	1	3	5	99	96	88	97
1	27	3	1	4	6	100	100	95	98
2	27	3	1	4	5	100	100	98	98
0	33	3	1	4	5	25	13	19	26
0	33	3	1	4	5	69	51	50	68
1	33	3	1	3	5	96	88	79	94
1	33	3	1	4	5	100	99	94	97
1	33	3	1	3	5	100	100	98	98
2	33	3	1	3	5	100	100	100	98
0	39	3	1	4	5	31	17	23	32
0	39	4	1	4	6	77	59	58	76
1	39	4	1	4	6	98	92	86	96
1	39	4	1	4	6	100	100	97	98
1	39	3	1	4	5	100	100	100	98
2	39	3	1	3	5	100	100	100	98
0	45	3	1	4	5	34	20	25	34
0	45	3	1	4	5	83	68	63	82
1	45	3	1	4	5	99	96	90	97
1	45	4	2	4	6	100	100	99	98
1	45	4	2	4	6	100	100	100	98
2	45	3	1	4	5	100	100	100	98

Tau plot

Code

mcplot(out, var_y = "es", var_x = 2, var_shape = 1)

Code

ggsave(filename = "figure-interventioneffect-tau.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1)

Tau table

Code

mctable(out, var_y = "es", wider = "statistic", format = "html")

		statistic 0				statistic 1
level_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
0.25	9	0.00	0.00	0.00	0.00	0.28	0.28	0.14	0.20
0.50	9	0.00	0.00	0.00	0.00	0.52	0.52	0.26	0.37
0.75	9	0.01	0.01	0.00	0.01	0.71	0.71	0.36	0.50
1.00	9	0.00	0.00	0.00	0.00	0.84	0.84	0.42	0.59
1.25	9	0.00	-0.01	-0.01	0.00	0.92	0.92	0.46	0.65
1.50	9	-0.01	0.00	0.00	0.00	0.97	0.96	0.48	0.68
0.25	12	0.00	0.00	0.00	0.00	0.27	0.27	0.13	0.18
0.50	12	-0.01	-0.01	-0.01	-0.01	0.52	0.53	0.25	0.35
0.75	12	-0.01	-0.01	0.00	0.00	0.71	0.71	0.35	0.47
1.00	12	-0.01	-0.01	0.00	0.00	0.84	0.84	0.41	0.55
1.25	12	-0.01	-0.01	0.00	0.00	0.92	0.92	0.45	0.60
1.50	12	-0.01	-0.01	0.00	0.00	0.96	0.96	0.47	0.64
0.25	15	0.01	0.01	0.01	0.00	0.27	0.27	0.13	0.19
0.50	15	0.00	0.00	0.00	0.00	0.52	0.52	0.25	0.35
0.75	15	0.00	0.00	0.00	0.00	0.71	0.71	0.34	0.48
1.00	15	-0.01	-0.01	-0.01	0.00	0.84	0.84	0.40	0.57
1.25	15	0.00	0.00	0.00	0.00	0.92	0.92	0.44	0.63
1.50	15	0.01	0.01	0.00	0.01	0.97	0.97	0.46	0.66
0.25	21	0.00	0.00	0.00	0.00	0.28	0.28	0.13	0.18
0.50	21	0.01	0.01	0.00	0.00	0.52	0.52	0.24	0.35
0.75	21	0.00	0.00	0.00	-0.01	0.70	0.70	0.33	0.47
1.00	21	0.00	0.00	0.00	0.00	0.84	0.84	0.39	0.56
1.25	21	0.00	0.00	0.00	0.00	0.92	0.92	0.43	0.62
1.50	21	0.00	-0.01	0.00	0.00	0.96	0.97	0.45	0.65
0.25	27	0.01	0.00	0.00	0.00	0.27	0.27	0.13	0.18
0.50	27	-0.01	-0.01	0.00	0.00	0.52	0.52	0.24	0.34
0.75	27	0.00	0.00	0.00	0.00	0.71	0.71	0.33	0.46
1.00	27	0.00	0.00	0.00	0.00	0.84	0.84	0.39	0.55
1.25	27	0.00	0.00	0.00	0.00	0.92	0.92	0.43	0.61
1.50	27	0.00	0.00	0.00	0.00	0.97	0.97	0.45	0.64
0.25	33	0.00	0.00	0.00	0.00	0.28	0.28	0.13	0.18
0.50	33	0.00	0.00	0.00	0.00	0.51	0.51	0.24	0.34
0.75	33	0.00	0.00	0.00	0.00	0.71	0.71	0.32	0.46
1.00	33	0.00	0.00	0.00	0.00	0.84	0.84	0.38	0.55
1.25	33	0.00	0.00	0.00	0.00	0.92	0.92	0.42	0.61
1.50	33	0.00	0.00	0.00	0.00	0.97	0.97	0.44	0.64
0.25	39	0.00	0.00	0.00	0.00	0.28	0.28	0.13	0.18
0.50	39	0.00	0.00	0.00	0.00	0.52	0.52	0.24	0.34
0.75	39	0.00	0.00	0.00	0.00	0.71	0.71	0.32	0.47
1.00	39	0.00	0.00	0.00	0.00	0.84	0.84	0.38	0.55
1.25	39	0.00	0.00	0.00	0.00	0.92	0.92	0.42	0.61
1.50	39	0.00	0.00	0.00	0.00	0.97	0.97	0.44	0.64
0.25	45	0.00	0.00	0.00	0.00	0.28	0.28	0.13	0.18
0.50	45	0.00	0.00	0.00	0.00	0.52	0.52	0.24	0.34
0.75	45	-0.01	-0.01	0.00	0.00	0.71	0.71	0.32	0.46
1.00	45	0.00	0.00	0.00	0.00	0.84	0.84	0.38	0.55
1.25	45	0.00	0.00	0.00	0.00	0.92	0.92	0.42	0.61
1.50	45	0.00	0.00	0.00	0.00	0.96	0.97	0.44	0.64

Strength of trend effect and level-effect

Code

design <- design_template(
    n = n_sims,
    start_value = 50,
    s = 10,
    level = level_effect * statistic,
    trend = trend_effect / length,
    slope = rnorm(n_sims, 0, abs(0.1/ (length* 2/3))),
    phase_design = list(A = length * 1/3, B = length * 2/3 ),
    distribution = "gaussian"
)

iterations <- iterations_template(
  trend_effect = c(-0.5, -0.25, 0, +0.25, +0.5),
  level_effect = c(0.25, 0.5, 0.75, 1, 1.25, 1.5),
  statistic = c(0, 1),
  length = 15,
  n_sims = 5000
)

out <- create_mc("trend-level.rds", 
                 design, iterations,
                 force_renew = FALSE)

Example plots

Code

ex_design <- design(
  n = 3,
  start_value = 50,
  s = 10,
  level = c(0.25, 0.5, 1),
  trend = c(-0.5/15, 0, 0.5/15),
  slope = rnorm(3, 0, abs(0.1 / 10)),
  phase_design = list(A = 5, B = 10),
  distribution = "gaussian"
)

ex <- random_scdf(ex_design,seed = 124)

ex_fn <- function(x) {
  scplot(x) %>% 
    set_yaxis(limits = c(40, 80)) %>%
    add_theme("basic")
}


ex_fn(ex[1])

Code

ex_fn(ex[2])

Code

ex_fn(ex[3])

Power plot

Code

mcplot(out, var_y = "p", var_x = 1, var_shape = 2, template = "power")

Code

ggsave(filename = "figure-trend-level.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Power table

Code

mctable(out, wider = "statistic", format = "html", digits = 0)

		statistic 0				statistic 1
trend_effect	level_effect	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
0	0	0	0	0	1	2	1	1	3
0	0	1	0	1	2	5	3	4	6
0	0	2	1	3	3	11	5	9	12
0	0	6	2	7	6	21	10	18	21
0	0	11	5	14	11	32	17	32	32
0	0	0	0	0	1	11	6	5	12
0	0	1	0	1	2	21	12	12	21
0	0	3	1	3	3	33	18	22	33
0	0	5	2	6	6	49	29	37	49
0	0	11	4	14	11	64	39	53	63
0	1	0	0	0	1	32	19	14	33
0	1	1	0	1	2	48	31	26	48
0	1	2	1	3	3	65	45	42	65
0	1	6	3	7	6	77	53	55	76
0	1	10	4	14	11	87	65	71	86
0	1	0	0	0	1	63	44	28	64
0	1	1	0	1	2	77	58	42	77
0	1	2	1	2	3	88	69	56	87
0	1	5	2	6	6	93	77	70	93
0	1	10	4	14	11	97	85	81	96
0	1	0	0	0	1	87	72	41	87
0	1	1	0	1	2	94	81	55	93
0	1	2	1	2	3	97	88	68	96
0	1	5	2	6	6	99	91	79	98
0	1	10	5	13	10	100	94	86	98
0	2	0	0	0	1	97	88	53	97
0	2	1	0	1	2	99	92	65	98
0	2	2	1	3	3	100	96	75	99
0	2	5	2	7	6	100	97	82	99
0	2	10	5	14	11	100	98	87	99

Tau plot

Code

mcplot(out, var_y = "es", var_x = 1, var_shape = 2)

Code

ggsave(filename = "figure-trend-level-tau.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Tau table

Code

mctable(out, var_y = "es", wider = "statistic", format = "html")

		statistic 0				statistic 1
trend_effect	level_effect	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
-0.50	0.25	-0.27	-0.26	-0.18	-0.18	0.00	0.02	-0.05	0.01
-0.25	0.25	-0.15	-0.14	-0.10	-0.10	0.14	0.15	0.04	0.10
0.00	0.25	0.00	0.00	0.00	0.00	0.27	0.27	0.13	0.19
0.25	0.25	0.14	0.14	0.09	0.10	0.41	0.40	0.22	0.27
0.50	0.25	0.27	0.26	0.18	0.18	0.51	0.49	0.29	0.34
-0.50	0.50	-0.27	-0.26	-0.18	-0.18	0.28	0.29	0.08	0.19
-0.25	0.50	-0.14	-0.13	-0.09	-0.09	0.40	0.40	0.16	0.27
0.00	0.50	0.01	0.01	0.00	0.01	0.52	0.52	0.25	0.35
0.25	0.50	0.14	0.13	0.09	0.09	0.62	0.61	0.32	0.42
0.50	0.50	0.27	0.26	0.18	0.18	0.70	0.69	0.39	0.47
-0.50	0.75	-0.28	-0.26	-0.18	-0.18	0.51	0.52	0.19	0.35
-0.25	0.75	-0.14	-0.13	-0.09	-0.09	0.62	0.63	0.27	0.42
0.00	0.75	0.00	0.00	0.00	0.00	0.71	0.72	0.34	0.49
0.25	0.75	0.14	0.14	0.10	0.10	0.78	0.77	0.39	0.53
0.50	0.75	0.27	0.26	0.18	0.18	0.84	0.82	0.45	0.57
-0.50	1.00	-0.28	-0.26	-0.18	-0.19	0.71	0.72	0.29	0.48
-0.25	1.00	-0.14	-0.14	-0.09	-0.09	0.78	0.79	0.35	0.53
0.00	1.00	0.00	0.00	0.00	0.00	0.85	0.84	0.40	0.58
0.25	1.00	0.14	0.13	0.09	0.09	0.89	0.88	0.45	0.60
0.50	1.00	0.27	0.25	0.18	0.18	0.92	0.90	0.49	0.62
-0.50	1.25	-0.26	-0.25	-0.18	-0.17	0.84	0.86	0.35	0.58
-0.25	1.25	-0.13	-0.13	-0.09	-0.09	0.89	0.90	0.39	0.61
0.00	1.25	0.00	0.00	0.00	0.00	0.92	0.92	0.44	0.63
0.25	1.25	0.14	0.13	0.09	0.10	0.95	0.94	0.48	0.65
0.50	1.25	0.27	0.25	0.18	0.18	0.96	0.95	0.51	0.66
-0.50	1.50	-0.27	-0.26	-0.18	-0.18	0.92	0.93	0.39	0.63
-0.25	1.50	-0.13	-0.12	-0.09	-0.09	0.95	0.95	0.43	0.65
0.00	1.50	-0.01	-0.01	-0.01	-0.01	0.97	0.96	0.46	0.66
0.25	1.50	0.14	0.13	0.09	0.09	0.98	0.97	0.49	0.67
0.50	1.50	0.27	0.26	0.18	0.18	0.98	0.97	0.52	0.67

Strength of trend effect and meassurement times

Code

design <- design_template(
    n = n_sims,
    start_value = 50,
    s = 10,
    level = level_effect * statistic,
    trend = trend_effect / length,
    slope = rnorm(n_sims, 0, 0.1 / (length * 2/3)),
    phase_design = list(A = length * 1/3, B = length * 2/3),
    distribution = "gaussian"
)

iterations <- list(
  trend_effect = c(-0.5, -0.25, 0, +0.25, +0.5),
  length = c(9, 12, 15, 21, 27, 33),
  statistic = c(0,1),
  level_effect = 1,
  n_sims = 5000
)

out <- create_mc("trend-length.rds", 
                 design, iterations,
                 force_renew = FALSE)

Example plots

Code

ex_design <- design(
  n = 3,
  start_value = 50,
  s = 10,
  level = 1,
  trend = c(-0.5/9, 0, 0.5/27),
  slope = rnorm(3, 0, abs(0.1 / c(6,10,28))),
  phase_design = list(A = c(3,5,9), B = c(6,10,18)),
  distribution = "gaussian"
)

ex <- random_scdf(ex_design,seed = 124)

ex_fn <- function(x) {
  scplot(x) %>% 
    set_yaxis(limits = c(40, 80)) %>%
    add_theme("basic")
}


ex_fn(ex[1])

Code

ex_fn(ex[2])

Code

ex_fn(ex[3])

Power plot

Code

mcplot(out, var_x = 1, var_shape = 2, template = "power")

Code

ggsave(filename = "figure-trend-length.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Power table

Code

mctable(out, var_y = "p", wider = "statistic", format = "html", digits = 0)

		statistic 0				statistic 1
trend_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
0	9	1	0	1	1	40	17	14	40
0	9	1	1	1	1	53	23	21	53
0	9	2	1	2	2	62	26	29	62
0	9	5	1	5	5	72	29	40	72
0	9	8	3	9	8	80	31	48	80
0	12	0	0	0	5	55	26	21	56
0	12	1	0	1	5	67	35	30	67
0	12	2	0	2	6	79	43	42	77
0	12	5	1	5	8	87	50	56	84
0	12	10	3	11	12	92	54	66	88
0	15	0	0	0	1	62	43	28	62
0	15	1	0	1	2	76	57	41	76
0	15	2	1	3	3	88	70	59	88
0	15	5	2	7	6	94	79	71	94
0	15	11	5	15	11	96	83	81	95
0	21	0	0	0	2	81	66	41	81
0	21	1	0	0	3	92	81	62	91
0	21	2	1	3	4	97	88	78	95
0	21	7	3	9	8	99	95	89	97
0	21	16	7	21	16	100	98	95	98
0	27	0	0	0	4	91	79	54	90
0	27	0	0	1	3	97	91	74	96
0	27	3	1	3	5	99	96	89	97
0	27	8	3	11	9	100	99	96	97
0	27	19	8	25	19	100	100	99	96
0	33	0	0	0	4	96	90	64	95
0	33	0	0	1	3	99	97	84	98
0	33	3	1	3	5	100	99	95	98
0	33	9	4	12	11	100	100	98	97
0	33	25	11	30	25	100	100	100	96

Tau plot

Code

mcplot(out, var_y = "es", var_x = 1, var_shape = 2)

Code

ggsave(filename = "figure-trend-length-tau.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Tau table

Code

mctable(out, var_y = "es", wider = "statistic", format = "html")

		statistic 0				statistic 1
trend_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
-0.50	9	-0.27	-0.25	-0.19	-0.19	0.70	0.72	0.30	0.50
-0.25	9	-0.13	-0.12	-0.09	-0.09	0.79	0.79	0.36	0.56
0.00	9	0.00	0.00	0.00	0.00	0.84	0.84	0.42	0.59
0.25	9	0.15	0.14	0.10	0.11	0.88	0.88	0.47	0.63
0.50	9	0.27	0.25	0.19	0.19	0.92	0.91	0.51	0.65
-0.50	12	-0.27	-0.26	-0.19	-0.16	0.71	0.72	0.29	0.48
-0.25	12	-0.14	-0.13	-0.09	-0.08	0.78	0.79	0.35	0.52
0.00	12	0.00	0.00	0.00	0.00	0.84	0.84	0.40	0.55
0.25	12	0.14	0.13	0.09	0.08	0.89	0.88	0.46	0.58
0.50	12	0.27	0.25	0.18	0.16	0.92	0.90	0.50	0.59
-0.50	15	-0.27	-0.26	-0.18	-0.18	0.70	0.71	0.28	0.48
-0.25	15	-0.14	-0.13	-0.09	-0.09	0.78	0.78	0.34	0.53
0.00	15	0.01	0.01	0.01	0.00	0.85	0.85	0.41	0.58
0.25	15	0.13	0.12	0.09	0.09	0.89	0.88	0.45	0.60
0.50	15	0.27	0.26	0.18	0.18	0.91	0.90	0.49	0.62
-0.50	21	-0.27	-0.25	-0.17	-0.17	0.70	0.72	0.28	0.48
-0.25	21	-0.14	-0.13	-0.09	-0.09	0.78	0.79	0.34	0.53
0.00	21	0.00	0.00	0.00	0.00	0.84	0.84	0.39	0.56
0.25	21	0.15	0.14	0.09	0.10	0.89	0.88	0.44	0.59
0.50	21	0.28	0.26	0.18	0.17	0.92	0.90	0.48	0.61
-0.50	27	-0.27	-0.26	-0.18	-0.16	0.70	0.72	0.27	0.47
-0.25	27	-0.14	-0.13	-0.09	-0.08	0.78	0.79	0.33	0.52
0.00	27	-0.01	-0.01	0.00	0.00	0.84	0.84	0.39	0.56
0.25	27	0.14	0.13	0.09	0.08	0.89	0.88	0.43	0.58
0.50	27	0.27	0.25	0.18	0.16	0.92	0.90	0.47	0.59
-0.50	33	-0.27	-0.25	-0.17	-0.16	0.71	0.72	0.27	0.48
-0.25	33	-0.14	-0.13	-0.09	-0.08	0.78	0.79	0.33	0.52
0.00	33	0.00	0.00	0.00	0.00	0.84	0.84	0.39	0.55
0.25	33	0.14	0.13	0.09	0.08	0.89	0.88	0.43	0.58
0.50	33	0.28	0.26	0.18	0.16	0.92	0.90	0.47	0.59

Strength of trend effect and meassurement times (equal phase length)

Code

design <- design_template(
    n = n_sims,
    start_value = 50,
    s = 10,
    level = level_effect * statistic,
    trend = trend_effect / length,
    slope = rnorm(n_sims, 0, 0.1 / (length * 2/3)),
    phase_design = list(A = length * 1/2, B = length * 1/2),
    distribution = "gaussian"
)

iterations <- list(
  trend_effect = c(-0.5, -0.25, 0, +0.25, +0.5),
  length = c(8, 12, 16, 22, 28, 34),
  statistic = c(0,1),
  level_effect = 1,
  n_sims = 5000
)

out <- create_mc("trend-length-2.rds", 
                 design, iterations,
                 force_renew = FALSE)

Power plot

Code

mcplot(out, var_x = 1, var_shape = 2, template = "power")

Code

ggsave(filename = "figure-trend-length-2.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Power table

Code

mctable(out, var_y = "p", wider = "statistic", format = "html", digits = 0)

		statistic 0				statistic 1
trend_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
0	8	1	0	1	5	42	31	30	46
0	8	1	1	1	5	54	36	35	55
0	8	3	2	3	5	65	40	40	64
0	8	6	4	5	8	74	41	45	72
0	8	10	5	8	11	82	41	49	79
0	12	0	0	0	4	57	49	38	59
0	12	1	1	1	4	71	58	49	71
0	12	2	2	2	5	83	64	57	81
0	12	6	4	5	7	90	68	64	87
0	12	9	6	8	10	95	70	68	91
0	16	0	0	0	5	75	66	57	76
0	16	1	1	1	5	87	75	68	87
0	16	3	2	3	6	95	83	79	92
0	16	6	4	6	8	98	87	85	94
0	16	14	7	11	14	99	89	89	94
0	22	0	0	0	4	88	83	72	88
0	22	1	1	1	3	96	90	84	95
0	22	3	2	3	4	99	94	91	97
0	22	8	4	6	9	100	97	95	97
0	22	19	10	15	19	100	98	98	96
0	28	0	0	0	5	96	91	85	95
0	28	0	0	1	4	99	96	92	98
0	28	2	2	3	5	100	98	97	97
0	28	9	5	9	10	100	99	99	97
0	28	23	11	18	22	100	100	100	96
0	34	0	0	0	7	98	97	92	98
0	34	0	0	1	5	100	99	97	98
0	34	2	2	3	5	100	100	99	98
0	34	11	6	9	12	100	100	100	97
0	34	27	14	22	26	100	100	100	95

Tau plot

Code

mcplot(out, var_y = "es", var_x = 1, var_shape = 2)

Code

ggsave(filename = "figure-trend-length-2-tau.png", width = 18, height = 18,  device='png', units = "cm", dpi=300, scale = 1.1)

Tau table

Code

mctable(out, var_y = "es", wider = "statistic", format = "html")

		statistic 0				statistic 1
trend_effect	length	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted	Tau-U A vs. B	Tau-U - trendA	Tau-U - trendA + trendB	Tau-U adjusted
-0.50	8	-0.28	-0.23	-0.16	-0.17	0.70	0.74	0.40	0.52
-0.25	8	-0.14	-0.12	-0.08	-0.08	0.78	0.80	0.45	0.57
0.00	8	0.00	0.00	0.00	0.00	0.84	0.84	0.48	0.60
0.25	8	0.15	0.12	0.08	0.10	0.88	0.86	0.50	0.63
0.50	8	0.28	0.23	0.16	0.17	0.92	0.87	0.52	0.65
-0.50	12	-0.28	-0.23	-0.15	-0.17	0.70	0.74	0.38	0.52
-0.25	12	-0.13	-0.11	-0.08	-0.08	0.78	0.80	0.43	0.57
0.00	12	0.00	0.00	0.00	0.00	0.84	0.84	0.46	0.60
0.25	12	0.15	0.12	0.08	0.09	0.89	0.86	0.48	0.63
0.50	12	0.27	0.23	0.15	0.17	0.92	0.87	0.50	0.64
-0.50	16	-0.28	-0.23	-0.15	-0.16	0.70	0.75	0.37	0.52
-0.25	16	-0.14	-0.11	-0.07	-0.08	0.78	0.80	0.42	0.56
0.00	16	0.00	0.01	0.00	0.01	0.85	0.85	0.45	0.60
0.25	16	0.14	0.11	0.07	0.08	0.89	0.87	0.47	0.62
0.50	16	0.27	0.22	0.15	0.15	0.92	0.87	0.49	0.63
-0.50	22	-0.27	-0.22	-0.14	-0.16	0.70	0.75	0.37	0.51
-0.25	22	-0.14	-0.11	-0.07	-0.09	0.78	0.80	0.41	0.56
0.00	22	0.00	0.00	0.00	0.00	0.84	0.84	0.44	0.59
0.25	22	0.14	0.11	0.07	0.08	0.89	0.86	0.46	0.63
0.50	22	0.27	0.23	0.14	0.16	0.92	0.87	0.48	0.64
-0.50	28	-0.27	-0.23	-0.14	-0.16	0.71	0.75	0.37	0.52
-0.25	28	-0.14	-0.12	-0.07	-0.08	0.78	0.80	0.40	0.56
0.00	28	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
0.25	28	0.14	0.11	0.07	0.08	0.89	0.86	0.46	0.62
0.50	28	0.27	0.22	0.14	0.15	0.92	0.88	0.48	0.63
-0.50	34	-0.27	-0.23	-0.14	-0.15	0.71	0.75	0.36	0.52
-0.25	34	-0.14	-0.12	-0.07	-0.08	0.78	0.81	0.40	0.56
0.00	34	0.00	0.00	0.00	0.00	0.84	0.84	0.43	0.59
0.25	34	0.14	0.12	0.07	0.08	0.89	0.86	0.46	0.61
0.50	34	0.27	0.23	0.14	0.14	0.92	0.87	0.47	0.62